On horizontal recurrent Finsler connections

Abstract

In this paper we adopt the pullback approach to global Finsler geometry. We investigate horizontally recurrent Finsler connections. We prove that for each scalar (\(\pi \))1-form A, there exists a unique horizontally recurrent Finsler connection whose h-recurrence form is A. This result generalizes the existence and uniqueness theorem of Cartan connection. We then study some properties of a special kind of horizontally recurrent Finsler connection, which we call special HRF-connection.